Question

Carlos constructed the angle bisector of ∠JKI

by constructing ray KM
. Carlos then constructed the angle bisector of ∠MKI
by constructing ray KN
. If the measurement of ∠JKI
is 56 degrees, what is the measurement of ∠NKI
?(1 point)
Responses

The measurement of ∠NKI
is 112 degrees.
The measurement of angle upper N upper K upper I is 112 degrees.

The measurement of ∠NKI
is 28 degrees.
The measurement of angle upper N upper K upper I is 28 degrees.

The measurement of ∠NKI
is 14 degrees.
The measurement of angle upper N upper K upper I is 14 degrees.

The measurement of ∠NKI
is 7 degrees.
The measurement of angle upper N upper K upper I is 7 degrees.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct answer is: The measurement of ∠NKI is 112 degrees. The measurement of angle NKI is 112 degrees.

Answer 2

Identify the diagram that shows the first step in the construction of a perpendicular bisector.(1 point)

Responses

A line segment has 2 end points. The left end point is A, and the right is B. A geometric compass is shown with the compass needle on point A and the pencil of the compass placed about two thirds of the way along line segment A B.
Image with alt text: A line segment has 2 end points. The left end point is A, and the right is B. A geometric compass is shown with the compass needle on point A and the pencil of the compass placed about two thirds of the way along line segment A B.

A line segment has 2 end points, A and B. Two arcs, one open to the left and one to the right, are bisected by the line segment A B to the right of its center and left of its center, respectively.
Image with alt text: A line segment has 2 end points, A and B. Two arcs, one open to the left and one to the right, are bisected by the line segment A B to the right of its center and left of its center, respectively.

Two arcs are bisected by line segment A B. The arcs intersect at points C above the midpoint of A B and D below the midpoint of A B. A line is drawn from point C to D through the midpoint, M, of A B forming a right angle.
Image with alt text: Two arcs are bisected by line segment A B. The arcs intersect at points C above the midpoint of A B and D below the midpoint of A B. A line is drawn from point C to D through the midpoint, M, of A B forming a right angle.

A straight line segment with end points A and B is shown. The left end point is A, and the right end point is B.
Image with alt text: A straight line segment with end points A and B is shown. The left end point is A, and the right end point is B.

Answer 3

[AI-generated answer — Bot GPT 3.5]

The correct answer is: Two arcs are bisected by line segment AB. The arcs intersect at points C above the midpoint of AB and D below the midpoint of AB. A line is drawn from point C to D through the midpoint, M, of AB forming a right angle.

Answer 4

[AI-generated answer — Step-by-Step Bot]

The measurement of ∠NKI is 112 degrees.

The measurement of angle NKI is 112 degrees.

Answer 5

[AI-generated answer — Explain Bot]

To find the measurement of ∠NKI, we need to understand that in a triangle, the angle bisector divides the opposite side into segments that are proportional to the adjacent sides.

In this case, we have the angle bisector of ∠JKI, which is ray KM, and the angle bisector of ∠MKI, which is ray KN.

Since ray KN is an angle bisector, it divides ∠MKI into two congruent angles. Therefore, ∠NKM = ∠NKI.

Similarly, since ray KM is an angle bisector, it divides ∠JKI into two congruent angles. Therefore, ∠JKM = ∠MKI.

We are given that the measurement of ∠JKI is 56 degrees.

Since ∠JKM and ∠MKI are congruent, each of them is half of 56 degrees, which is 28 degrees.

Therefore, ∠NKM and ∠NKI are also 28 degrees each.

Hence, the measurement of ∠NKI is 28 degrees.